The master for a stereo record is generally cut by a cutting stylus which is driven inwardly in a straight line along a radius of the record. Thus the cutting stylus executes a transverse movement to provide the spiral grooves and is driven in such a manner that with respect to the sides of the grooves made, the stylus simultaneously contacts both sides of the groove along a radius. It will therefore be appreciated that at any instant of time opposing sides of a groove are formed by motion of a stylus which simultaneously contacts opposing sides of the groove along the record radius. Note that the stylus is in effect drawn tangent to the groove.
In consequence, the inward lateral or transverse motion of the cutting stylus when the original lacquered master is made always takes place along a radius of the record, which is the line passing through the stylus tip and the turntable spindle. It will be appreciated that the only way to obtain an identical waveform out of the terminals of a playback cartridge as went into the terminals of the cutter head is to duplicate this lateral motion without any angular errors at the tip of the playback stylus. This duplication is impossible with conventional pivoted tone arms because they move in an arc as opposed to being moved laterally across the record.
If, as is the case in all pivoted tone arms, the lateral motion of the playback stylus is not exactly along a radius, the result is not only simple harmonic inter-modulation distortion, as has been popularly assumed, but also frequency inter-modulation and frequency cross-modulation distortion, which are time dispersive and therefore much more audible and disturbing.
If a reference signal, for instance coming from a phonograph record, is riddled with frequency inter-modulation and frequency cross-modulation distortion, a listener cannot tell how good or bad the components are that he is listening to. Therefore, all subjective evaluations of audio equipment where phonograph records are the program source must be considered highly suspect unless the cartridge has been aligned within 0.005 inches. It will be appreciated that one way to make virtually certain that the cartridge is misaligned is to mount it dead straight ahead and trued up in the head shell of a tone arm that in turn is mounted on the turntable. This is because almost all commercially available tone arms have head shells which are not aligned in the appropriate manner.
When the stylus is mounted so as to minimize the angular error at the tip of the playback stylus, there is an unexpected benefit especially in a large percentage of 12 inch LP records both old and new which will sound excellent when the information in their grooves is extracted unaltered by cartridge alignment error. In general, gross cartridge misalignment can result in up to 10% total harmonic distortion which is unacceptable.
Most record changers or turntables are provided with a rigid pivoted tone arm which must swing in an arc and therefore cannot possibly track radially as is the case when the lateral cutter is used. What may be less obvious is the precise relationship between the resultant tracking error and the corrective offset angle/overhang geometry of a typical tone arm. A typical mistake is to assume that it is the tracking error that must be minimized. Actually, it is the tracking distortion, which happens to be directly proportional to the tracking error but inversely proportional to the radial distance of the groove from the spindle. Consequently what must be minimized is the "ratio" of the tracking error to its radial distance. The correct way to formulate the basic mathematical question about optimum lateral tracking geometry is therefore the following: with a tone arm of given effective length, over a total recorded area of given maximum and minimum radii, the question is what combination of off-set angle and overhang will yield the smallest possible peak values of the ratio of the tracking error to groove radius. In 1941 this question was definitively solved by H. G. Baerwald in which he defined two points at which the alignment of the cartridge is to be such that the cartridge is tangent to the grooves at these two points. These are said to be zero-error points, with the first about 1/3 of the way into the recording area, and the second close to but still a small distance away from the inner most groove. What he found was that with optimum offset angle and overhang, these zero points are fixed regardless of arm length, as long as the maximum and minimum radii of the recorded area are specified and that a tone arm cartridge aligned to these points resulted in the smallest possible peak values of tracking distortion as set forth above. Thus correct tone arm geometry is not a matter of opinion in that for any given set of conditions there exists only one optimum solution.
For a 30 centimeter LP record with a recorded area between the IEC standard maximum and minimum radii of 146.05 and 60.32 mm, zero tracking error can be obtained in all cases at radii of 120.9 mm and 66.0 mm. Table 1 reproduced hereinbelow relates the effective arm length, optimum overhang and optimum offset angle required to achieve zero tracking error at the two aforesaid points.
TABLE 1 ______________________________________ Effective Optimum Optimum Effective Optimum Arm Over- Offset Arm Optimum Offset Length hang Angle Length Overhang Angle (mm) (mm) (.degree.) (mm) (mm) (.degree.) ______________________________________ 200 21.1 27.9 238 17.4 23.1 201 20.9 27.7 239 17.3 23.1 202 20.8 27.6 240 17.2 22.9 203 20.7 27.4 241 17.2 22.8 204 20.6 27.3 242 17.1 22.7 205 20.5 27.1 243 17.0 22.6 206 20.4 27.0 244 16.9 22.5 207 20.3 26.8 245 16.9 22.4 208 20.2 26.7 246 16.8 22.3 209 20.0 26.6 247 16.7 22.2 210 19.9 26.4 248 16.6 22.1 211 19.8 26.3 249 16.6 22.0 212 19.7 26.2 250 16.5 21.9 213 19.6 26.0 251 16.4 21.9 214 19.5 25.9 252 16.4 21.8 215 19.4 25.8 253 16.3 21.7 216 19.3 25.6 254 16.2 21.6 217 19.2 25.5 255 16.2 21.5 218 19.1 25.4 256 16.1 21.4 219 19.0 25.3 257 16.0 21.3 220 18.9 25.1 258 16.0 21.2 221 18.9 25.0 259 15.9 21.1 222 18.8 24.9 260 15.8 21.1 223 18.7 24.8 261 15.8 21.0 224 18.6 24.7 262 15.7 20.9 225 18.5 24.5 263 15.6 20.8 226 18.4 24.4 264 15.6 20.7 227 18.3 24.3 265 15.5 20.6 228 18.2 24.2 266 15.4 20.6 229 18.1 24.1 267 15.4 20.5 230 18.1 24.0 268 15.3 20.4 231 18.0 23.9 269 15.3 20.3 232 17.9 23.8 270 15.2 20.2 233 17.8 23.6 271 15.1 20.2 234 17.7 23.5 272 15.1 20.1 235 17.6 23.4 273 15.0 20.0 236 17.6 23.3 274 15.0 19.9 237 17.5 23.2 275 14.9 19.9 ______________________________________
As can be seen the measurements necessary are time consuming and difficult when utilizing machinist scales which are necessary in order to obtain a no greater position error than 0.005 inches.
In the past at least one alignment tool has utilized the Baerwald two point system to simplify the alignment of cartridges within their head shells. This alignment tool is manufactured by Dennesen and utilizes a translatable trammel, at the end of which is affixed a pointer. The trammel is releaseably mounted to a base which has a spindle hole and a point at the 66 millimeter Baerwald point. This jig operates on the finding, pointed out in the Audio Critic; volume 1, No. 6, Spring through Fall 1978, page 46, that with respect to the computations of Table I, the product of the effective arm length and the sine of the optimum offset angle are constant and equal to 93.4 millimeters. This length corresponds to the length of the perpendicular from the lateral pivot point of the tone arm to the rearward extension of the long axis of the cartridge.
As will be appreciated, utilizing the Dennesen alignment tool, the base is first placed over the spindle and the trammel is then moved backward and forward until the pointer is directly over the pivot point for the tone arm. While alignment utilizing machinist scales took as much as 21/2hours, the Dennesen device permits cartridge alignment within several minutes.
By way of background, the Dennesen device required optical alignment of the pointer by viewing the point of the pointer from positions on all sides of the pivot point of the tone arm. As such, the pointer/pivot relationship is determined by viewing the pointer at one point, and the possibility for error is great since this single point system provides an inadequate reference for accurately fixing the trammel/pointer directly over the tone arm pivot point. The trammel must be moved in a groove in its base and then must be tightened down at the appropriate point which requires considerable manual dexterity. Moreover, it should be pointed out, that the Dennesen device utilizes the inner of the two Baerwald points and operates the trammel from a position on the opposite side of the spindle from the side at which the Baerwald point is located.
By way of reference, the original computations of H.G. Baerwald are carried in the December 1941 issue of the "Journal of the Society of Motion Picture Engineers".